Catalysts for the oxidative purification of exhaust gases such as the exhaust gases from internal combustion engines, are prepared by applying a suspension whose solid content consists essentially of boehmite to a ceramic support body thereby forming an intermediate coating which is adapted to receive one or more metals of the platinum group or alloys thereof in finely divided form. The thus treated support body is thereafter heated. The coating suspension also can contain dissolved aluminum nitrate. The intermediate coating of boehmite on the support body is converted to active aluminum oxide prior to impregnation with one or more metals of the platinum group or alloys thereof in finely divided form or the conversion can take place after such impregnation, for example, by heating upon exposure to the hot exhaust gases of an internal combustion engine.